iPhone SE inaccurate reporting of battery percentage

Bought a used SE 1st gen as a spare phone. Phone was shutting down at high battery percentages. Tried to recalibrate it by charging to 100% and draining down to 1% several times. I'm now seeing unrealistic drop in percentage when doing anything demanding. E.g battery is at 70%, browse App Store for a few minutes and it quickly drops to 55%. Reboot phone and it's back up to 69% without charging. If I use the phone without turning it off at all, I see a fast drop to 1% but then it stays at that for many hours before dying.

Battery capacity 79% in settings, apparently supporting normal peak performance despite previous abrupt shutdowns at high percentages. 3uTools shows 1101 charge cycles and 2016 production date so it does definitely need a new battery which I'm happy to get, but just want to make sure this will solve the problem and there's nothing more sinister going on as I've never had a battery behave in this way before. Charges normally, syncs with iTunes fine.

Any thoughts greatly appreciated :)